The front shock absorber of a typical mountain bike (see Figure 4.2) may be modeled as a spring-dashpot system. A typica
Posted: Thu Feb 17, 2022 11:08 am
The front shock absorber of a typical mountain bike (see Figure
4.2) may be modeled as a spring-dashpot system. A typical value for
the spring constant might be k = 15000 newtons per meter with a
damping constant c = 1700 newtons per meter per second; we’ll
explore this model more in later examples and the Modeling Projects
in Section 4.6. The mass in this system consists of the rider’s
mass and the bike’s mass, less the mass of the wheels since they
are not suspended by the shock absorber. Suppose the rider has a
mass of 80 kg, the bike (less wheels) has a mass of 12 kg, and that
half of this total mass is supported by the front shock absorber,
so the effective supported mass is m = (80+12)/2 = 46 kg. Assume
that the only other force acting on the rider is gravity. If the
front wheel is in contact with the ground, it may be considered
fixed or immovable, and if u(t) denotes the vertical displacement
of the front shock from equilibrium then (4.3) becomes. • Has a
spring that is as compliant (least stiff) as possible, but yields a
shock displacement of no more than 140 mm when the rider rides off
a 1.5 meter drop. • Is not excessively overdamped (which makes
riding on rugged terrain feel harsh) or under- damped (which makes
the bike feel too bouncy.) my''(t) +cy'(t) +ky(t) = −mg, (4.119)
where m = 46 kg and g = 9.8. Question: Experiment.
Can you find other values for c and k that subject the rider to
less acceleration while not bottoming out the shock in a 1.5 meter
drop?
4.2) may be modeled as a spring-dashpot system. A typical value for
the spring constant might be k = 15000 newtons per meter with a
damping constant c = 1700 newtons per meter per second; we’ll
explore this model more in later examples and the Modeling Projects
in Section 4.6. The mass in this system consists of the rider’s
mass and the bike’s mass, less the mass of the wheels since they
are not suspended by the shock absorber. Suppose the rider has a
mass of 80 kg, the bike (less wheels) has a mass of 12 kg, and that
half of this total mass is supported by the front shock absorber,
so the effective supported mass is m = (80+12)/2 = 46 kg. Assume
that the only other force acting on the rider is gravity. If the
front wheel is in contact with the ground, it may be considered
fixed or immovable, and if u(t) denotes the vertical displacement
of the front shock from equilibrium then (4.3) becomes. • Has a
spring that is as compliant (least stiff) as possible, but yields a
shock displacement of no more than 140 mm when the rider rides off
a 1.5 meter drop. • Is not excessively overdamped (which makes
riding on rugged terrain feel harsh) or under- damped (which makes
the bike feel too bouncy.) my''(t) +cy'(t) +ky(t) = −mg, (4.119)
where m = 46 kg and g = 9.8. Question: Experiment.
Can you find other values for c and k that subject the rider to
less acceleration while not bottoming out the shock in a 1.5 meter
drop?